Goddyn, Luis; Richter, R. Bruce and Širáň, Jozef
Triangular embeddings of complete graphs from graceful labellings of paths.
Journal of Combinatorial Theory, Series B, 97(6) pp. 964–970.
We show that to each graceful labelling of a path on 2s+1 vertices, s≥2, there corresponds a current assignment on a 3-valent graph which generates at least 22s cyclic oriented triangular embeddings of a complete graph on 12s+7 vertices. We also show that in this correspondence, two distinct graceful labellings never give isomorphic oriented embeddings. Since the number of graceful labellings of paths on 2s+1 vertices grows asymptotically at least as fast as (5/3)2s, this method gives at least 11s distinct cyclic oriented triangular embedding of a complete graph of order 12s+7 for all sufficiently large s.
Actions (login may be required)